Smooth Dial or Ten Notches

A payout terminal offers two modes, and you must pick one before pressing the button. Mode A pays a dollar amount drawn uniformly from the continuous interval [0,10][0, 10]. Mode B pays a whole-dollar amount drawn uniformly from the integers {0,1,2,…,10}\{0, 1, 2, \dots, 10\}. Is one mode better than the other? Which would you pick, and why?

Answer

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